%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM641^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:16:40 AM UTC 2026
% Result : Theorem 0.08s 0.15s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 9 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 9 ( 8 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 28 ( 4 ~; 0 |; 0 &; 24 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 2 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 6 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_23,type,
x: nat ).
thf(decl_24,type,
suc: nat > nat ).
thf(decl_25,type,
pl: nat > nat > nat ).
thf(decl_26,type,
n_1: nat ).
thf(satz4g,conjecture,
( ( suc @ x )
= ( pl @ n_1 @ x ) ),
file('/export/starexec/sandbox2/tmp/tmp.LRet06X2Fv/E---3.1_20348.p',satz4g) ).
thf(satz4c,axiom,
! [X1: nat] :
( ( pl @ n_1 @ X1 )
= ( suc @ X1 ) ),
file('/export/starexec/sandbox2/tmp/tmp.LRet06X2Fv/E---3.1_20348.p',satz4c) ).
thf(c_0_2,negated_conjecture,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(assume_negation,[status(cth)],[satz4g]) ).
thf(c_0_3,negated_conjecture,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(fof_simplification,[status(thm)],[c_0_2]) ).
thf(c_0_4,negated_conjecture,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(fof_nnf,[status(thm)],[c_0_3]) ).
thf(c_0_5,plain,
! [X3: nat] :
( ( pl @ n_1 @ X3 )
= ( suc @ X3 ) ),
inference(variable_rename,[status(thm)],[satz4c]) ).
thf(c_0_6,negated_conjecture,
( ( suc @ x )
!= ( pl @ n_1 @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
thf(c_0_7,plain,
! [X1: nat] :
( ( pl @ n_1 @ X1 )
= ( suc @ X1 ) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
thf(c_0_8,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_6,c_0_7])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUM641^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.02 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 12:21:48 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.13 Running higher-order theorem proving
% 0.08/0.14 Running: /export/starexec/sandbox2/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/tmp/tmp.LRet06X2Fv/E---3.1_20348.p
% 0.08/0.15 % Version: 3.5.1-ho
% 0.08/0.15 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.15 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.15 % Starting sh4l with 300s (1) cores
% 0.08/0.15 % Starting ehoh_best_nonlift_rwall with 300s (1) cores
% 0.08/0.15 % sh4l with pid 20363 completed with status 0
% 0.08/0.15 % Result found by sh4l
% 0.08/0.15 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.15 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.15 % Starting sh4l with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HUUPF-FFSF21-SFFFFFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % SubtermCWHack with pid 20368 completed with status 0
% 0.08/0.15 % Result found by SubtermCWHack
% 0.08/0.15 % Preprocessing class: HSSSSMSSSSSNFFN.
% 0.08/0.15 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.15 % Starting new_ho_10 with 1500s (5) cores
% 0.08/0.15 % Starting ho_unfolding_6 with 300s (1) cores
% 0.08/0.15 % Starting sh4l with 300s (1) cores
% 0.08/0.15 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.15 % No SInE strategy applied
% 0.08/0.15 % Search class: HUUPF-FFSF21-SFFFFFNN
% 0.08/0.15 % Scheduled 7 strats onto 1 cores with 300 seconds (300 total)
% 0.08/0.15 % Starting SubtermCWHack with 28s (1) cores
% 0.08/0.15 % Preprocessing time : 0.001 s
% 0.08/0.15
% 0.08/0.15 % Proof found!
% 0.08/0.15 % SZS status Theorem
% 0.08/0.15 % SZS output start CNFRefutation
% See solution above
% 0.08/0.15 % Parsed axioms : 7
% 0.08/0.15 % Removed by relevancy pruning/SinE : 0
% 0.08/0.15 % Initial clauses : 7
% 0.08/0.15 % Removed in clause preprocessing : 5
% 0.08/0.15 % Initial clauses in saturation : 2
% 0.08/0.15 % Processed clauses : 2
% 0.08/0.15 % ...of these trivial : 0
% 0.08/0.15 % ...subsumed : 0
% 0.08/0.15 % ...remaining for further processing : 1
% 0.08/0.15 % Other redundant clauses eliminated : 0
% 0.08/0.15 % Clauses deleted for lack of memory : 0
% 0.08/0.15 % Backward-subsumed : 0
% 0.08/0.15 % Backward-rewritten : 0
% 0.08/0.15 % Generated clauses : 0
% 0.08/0.15 % ...of the previous two non-redundant : 0
% 0.08/0.15 % ...aggressively subsumed : 0
% 0.08/0.15 % Contextual simplify-reflections : 0
% 0.08/0.15 % Paramodulations : 0
% 0.08/0.15 % Factorizations : 0
% 0.08/0.15 % NegExts : 0
% 0.08/0.15 % Equation resolutions : 0
% 0.08/0.15 % Disequality decompositions : 0
% 0.08/0.15 % Total rewrite steps : 1
% 0.08/0.15 % ...of those cached : 0
% 0.08/0.15 % Propositional unsat checks : 0
% 0.08/0.15 % Propositional check models : 0
% 0.08/0.15 % Propositional check unsatisfiable : 0
% 0.08/0.15 % Propositional clauses : 0
% 0.08/0.15 % Propositional clauses after purity: 0
% 0.08/0.15 % Propositional unsat core size : 0
% 0.08/0.15 % Propositional preprocessing time : 0.000
% 0.08/0.15 % Propositional encoding time : 0.000
% 0.08/0.15 % Propositional solver time : 0.000
% 0.08/0.15 % Success case prop preproc time : 0.000
% 0.08/0.15 % Success case prop encoding time : 0.000
% 0.08/0.15 % Success case prop solver time : 0.000
% 0.08/0.15 % Current number of processed clauses : 1
% 0.08/0.15 % Positive orientable unit clauses : 1
% 0.08/0.15 % Positive unorientable unit clauses: 0
% 0.08/0.15 % Negative unit clauses : 0
% 0.08/0.15 % Non-unit-clauses : 0
% 0.08/0.15 % Current number of unprocessed clauses: 0
% 0.08/0.15 % ...number of literals in the above : 0
% 0.08/0.15 % Current number of archived formulas : 0
% 0.08/0.15 % Current number of archived clauses : 0
% 0.08/0.15 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.15 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.15 % Non-unit clause-clause subsumptions : 0
% 0.08/0.15 % Unit Clause-clause subsumption calls : 0
% 0.08/0.15 % Rewrite failures with RHS unbound : 0
% 0.08/0.15 % BW rewrite match attempts : 0
% 0.08/0.15 % BW rewrite match successes : 0
% 0.08/0.15 % Condensation attempts : 0
% 0.08/0.15 % Condensation successes : 0
% 0.08/0.15 % Termbank termtop insertions : 144
% 0.08/0.15 % Search garbage collected termcells : 6
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.002 s
% 0.08/0.15 % System time : 0.000 s
% 0.08/0.15 % Total time : 0.002 s
% 0.08/0.15 % Maximum resident set size: 3628 pages
% 0.08/0.15
% 0.08/0.15 % -------------------------------------------------
% 0.08/0.15 % User time : 0.004 s
% 0.08/0.15 % System time : 0.001 s
% 0.08/0.15 % Total time : 0.005 s
% 0.08/0.15 % Maximum resident set size: 4864 pages
% 0.08/0.15 % E exiting
%------------------------------------------------------------------------------